1. Option Pricing Junya Namai

2. Agenda  Current Option Price for Netflix  Binomial Model for Stock  Binomial Options Pricing for Call Option  Binomial Options Pricing for Put Option  Binomial Options Pricing for Call Option – Multi period  Black-Scholes Model  Quiz  Questions

3. Current Option Price for Netflix  http://finance.yahoo.com/q/op?s=NFLX&m=2013-05 http://finance.yahoo.com/q/op?s=NFLX&m=2013-05

4. Binomial Model for Stock t0t0 t1t1 up down $80 $55 P(u) = 0.6 P(d) = 0.4 r = 0.08

5. Binomial options pricing for Call Option t0t0 t1t1 up down $80 $55 P(u) = 0.6 P(d) = 0.4 K = $70 $10 $0 r = 0.08 Max(0, Price - K)

6. Binomial options pricing for Put Option t0t0 t1t1 up down $80 $55 P(u) = 0.6 P(d) = 0.4 K = $70 $0 $15 r = 0.08 Max(0, K-Price)

7. Call Option - Multi Period t0t0 t1t1 t2t2 t3t3 t4t4 $90 $80 $70 $60 $50 P(u) = 0.6 P(d) = 0.4 K = $70 r = 0.08 0.6 0.4 0.6 $20 $10 $0 Max(0, Price-K)

8. Call Option - Multi Period t4t4 $90 $80 $70 $60 $50 Path 1 4 6 4 1 call $20 $10 $0 4ups 3ups + 1down 2ups + 2downs 3downs + 1up 4downs

9. Call Option - Multi Period

10. Binomial Distribution (Pascal's triangle)

11. Black-Scholes Formula (5 parameters)  Stock Price  Exercise (Strike) Price  Time to Expiration  Volatility of Stock  Risk-Free Rate

12. Black-Scholes Formula

14. Binomial vs Black-Scholes  Binomial  Flexible  Finite steps  Discrete  Values American  Values complexities  Black-Scholes  Limited  Infinite  Continuous

15. Quick Quiz 1  If volatility of stock price becomes higher, does the option price go up or down?  Black-Scholes Calculator Black-Scholes Calculator

16. Lognormal Distribution

17. Quick Quiz 2  If interest rates becomes higher, does the option price go up or down?

18. Question

19. Reference  http://stattrek.com/probability-distributions/binomial.aspx http://stattrek.com/probability-distributions/binomial.aspx  http://en.wikipedia.org/wiki/Binomial_distribution http://en.wikipedia.org/wiki/Binomial_distribution  http://www.tradingtoday.com/black- scholes?callorput=c&strike=70&stock=70&time=180&volatility =48&interest=8 http://www.tradingtoday.com/black- scholes?callorput=c&strike=70&stock=70&time=180&volatility =48&interest=8  http://en.wikipedia.org/wiki/Binomial_options_pricing_model http://en.wikipedia.org/wiki/Binomial_options_pricing_model  http://www.optiontradingpedia.com/free_black_scholes_model.htm http://www.optiontradingpedia.com/free_black_scholes_model.htm  http://www.optiontradingpedia.com/free_black_scholes_model.htm http://www.optiontradingpedia.com/free_black_scholes_model.htm  http://easycalculation.com/statistics/binomial-distribution.php http://easycalculation.com/statistics/binomial-distribution.php  http://www.hoadley.net/options/bs.htm http://www.hoadley.net/options/bs.htm

20. Risk-Neutral Valuation (Backup)

23. Up and Down Changes to STD